Reduce the fraction $\frac{2}{16}$ to lowest terms by extracting and canceling out $2$.
$$\sqrt{\frac{1}{8}}$$
Rewrite the square root of the division $\sqrt{\frac{1}{8}}$ as the division of square roots $\frac{\sqrt{1}}{\sqrt{8}}$.
$$\frac{\sqrt{1}}{\sqrt{8}}$$
Calculate the square root of $1$ and get $1$.
$$\frac{1}{\sqrt{8}}$$
Factor $8=2^{2}\times 2$. Rewrite the square root of the product $\sqrt{2^{2}\times 2}$ as the product of square roots $\sqrt{2^{2}}\sqrt{2}$. Take the square root of $2^{2}$.
$$\frac{1}{2\sqrt{2}}$$
Rationalize the denominator of $\frac{1}{2\sqrt{2}}$ by multiplying numerator and denominator by $\sqrt{2}$.
